A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 6.
When 12 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 9 : 8.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 8 = (3) |
(1) 10-cent |
(2) 50-cent |
Make p the same. (2) x 9 = (4) |
Before |
40 u |
5 u |
6 u |
54 u |
Change |
+ 480 |
+ 60 |
- 12 |
- 108 |
After |
72 p |
9 p |
8 p |
72 p |
Value of 12 fifty-cent coins
= 12 x 50
= 600¢
Number of ten-cent coins to exchange for
= 600 ÷ 10
= 60
5 u + 60 = 9 p --- (1)
6 u - 12 = 8 p --- (2)
Make p the same.
(1)
x 8 40 u + 480 = 72 p --- (3)
(2)
x 9 54 u - 108 = 72 p --- (4)
(4) = (3)
54 u - 108 = 40 u + 480
54 u - 40 u = 480 + 108
14 u = 588
1 u = 588 ÷ 14 = 42
Value of ten-cent coins
= 5 u x 10
= 5 x 42 x 10
= 2100¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 42 x 50
= 12600¢
Total value of coins
= 2100 + 12600
= 14700¢
100¢ = $1
Sum of money in the coin box
= 14700¢
= $147
Answer(s): $147